A Study Evaluating the Effects of GLPG3667 Administered as Oral Treatment in Adult Participants With Active Systemic Lupus Erythematosus

Key Inclusion Criteria: 1. Participant with documented diagnosis of SLE as defined by the 2019 European League Against Rheumatism (EULAR)/American College of Rheumatology (ACR) classification criteria with a disease diagnosed ≥24 weeks before the screening visit. 2. Participant has a total Systemic Lupus Erythematosus Disease Activity Index 2000 (SLEDAI-2K) score ≥6 points and a clinical SLEDAI-2K score ≥4 at screening and baseline (scores must be confirmed by central review at screening). * Lupus headache, alopecia, organic brain syndrome, and mucous membrane ulceration will not count toward the score required for screening at entry. * Clinical SLEDAI-2K excludes laboratory abnormalities such as hematuria, pyuria, urinary casts, proteinuria, positive anti-double-stranded deoxyribonucleic acid (anti-dsDNA), decreased complement, thrombocytopenia, and leukopenia. 3. Participant is positive for 1 of the following: antinuclear antibodies (ANA) ≥1:80 or positive anti-dsDNA (indeterminate values are considered positive), or positive anti-Smith (anti-Sm), as determined by the central laboratory. 4. At least 1 of the following BILAG-based protocol-specific manifestations of SLE: * BILAG A or B score in the mucocutaneous body system. * BILAG A or B score in the musculoskeletal body system due to arthritis. * If only 1 B and no A score is present in the mucocutaneous body system or in the musculoskeletal body system due to arthritis, then at least 1 B score must be present in one of the other body systems, for a total of \>=2 BILAG B body system scores. 5. Background therapy with at least 1 of the following medications is required for \>=12 weeks before the screening visit and must remain stable until randomization and throughout study participation: * 1 immunosuppressant (combination of immunosuppressants is not permitted), stable at least 8 weeks prior to screening. * 1 antimalarial, stable at least 8 weeks prior to screening. In addition, oral corticosteroids (CS) (prednisone or equivalent) and/or NSAIDs background therapy is permitted but not required: * CS (prednisone or equivalent; \<=30 mg/day; CS monotherapy is not permitted), stable at least 2 weeks prior to screening; AND/OR * Non-steroidal anti-inflammatory drugs (NSAIDs; NSAIDs monotherapy is not permitted), stable at least 2 weeks prior to screening. Key Exclusion Criteria: 1. Participant with active, severe lupus nephritis (World Health Organization Class III, IV) that requires or may require treatment with cytotoxic agents or high-dose CS are excluded. 2. Participants with pre-existing, controlled renal disease with serum creatinine≥ 2 x upper limit of normal (ULN) and either residual proteinuria up to 3 grams/day (g/day) or a urine protein: creatinine ratio (UPCR) of up to 3 milligrams/milligrams (mg/mg) or 339 milligrams of albumin per millimole of creatinine (mg/mmol) are allowed. Control of renal disease must be documented with at least 2 measurements of proteinuria or UPCR over the past 6 months. 3. Participants with a history of catastrophic antiphospholipid syndrome are excluded. This includes Participants with a serious thrombotic event (e.g. pulmonary embolism, stroke, deep vein thrombosis) or unexplained pregnancy loss within 1 year before the screening visit or history of 3 or more unexplained consecutive pregnancy losses. Participants with antiphospholipid antibody syndrome on stable anticoagulant therapy at an effective dose are allowed. 4. Participants with active or unstable lupus neuropsychiatric manifestations, including but not limited to any condition defined by BILAG A criteria are excluded, with the exception of participants with mononeuritis multiplex and polyneuropathy, who are allowed. 5. Drug-induced SLE. 6. Participant has a chronic hepatitis B virus (HBV) infection, as defined by positive HBV surface antigen (HBsAg) at screening and detectable HBV core antibody (HBcAb). 7. Participant has chronic hepatitis C virus (HCV) infection, as defined by positive HCV antibody (Ab) at screening and detectable HCV viremia. Participants with positive HCV Ab must undergo reflex HCV ribonucleic acid (RNA) testing, and Participants with HCV RNA positivity will be excluded. Participants with positive HCV Ab and negative HCV RNA are eligible. 8. Participant has a history of or a current immunosuppressive condition or a history of opportunistic infections (e.g. human immunodeficiency virus \[HIV\] infection, histoplasmosis, listeriosis, coccidioidomycosis, pneumocystosis, aspergillosis, herpes simplex, herpes zoster). 9. Participant testing positive for severe acute respiratory syndrome coronavirus disease 2 (SARS-CoV-2) infection, even if fully vaccinated against SARS-CoV-2, as detected by rapid antigen testing and/or revert transcription polymerase chain reaction (RT-PCR), test at screening and/or baseline (Day 1). Participant presenting any signs or symptoms suggestive of SARS-CoV-2 infection, as detected at screening or baseline following careful physical examination (e.g. cough, fever, headaches, fatigue, dyspnoea, myalgia, anosmia, dysgeusia, anorexia, sore throat), should undergo testing even if fully vaccinated against SARS-CoV-2, as per locally applicable standard diagnostic criteria to diagnose SARS-CoV-2 infection and excluded if positive. 10. Participant meets 1 of the following tuberculosis (TB) criteria at screening: * A history of active or currently active TB (regardless of treatment). * A positive QuantiFERON®-TB Gold Plus In-tube test at screening unless the investigator assesses this is due to a documented history of adequately treated latent TB infection. Note: If the test result is indeterminate, it may be repeated once; if indeterminate or positive on retest, Participant is not eligible. 11. Participant with poorly controlled chronic cardiac, pulmonary, or renal disease. 12. Participant has at screening, presence of severe renal impairment (defined as estimated glomerular filtration rate \[eGFR\] \<30 mL/minute/1.73 m2, using the Chronic Kidney Disease Epidemiology equation). 13. Prior exposure to tyrosine kinase 2 (TYK2) inhibitors. 14. Female participant is pregnant or breast feeding or intending to become pregnant or breastfeed during the study. 15. Participant has taken any prohibited therapies within the defined washout periods before screening, and during screening.